Effect of magnetic perturbations on tokamak divertors

The magnetic footprint on collector plates in a tokamak divertor is heavily constrained by the field lines obeying the equations of 112 degree of freedom Hamiltonian mechanics. In a tokamak with broken axisymmetry, the last toroidal surface on which all field lines are confined encloses less toroidal flux than the ideal axisymmetric separatrix. The location of this surface is determined by the amplitude of the perturbations that resonate with the safety factor, q. Near a separatrix, such as that of a tokamak divertor, q has a logarithmic singularity as a function of the enclosed toroidal flux. The resonant perturbations produce islands in the field line trajectories that must overlap to fundamentally change the properties of the field line trajectories by making the field lines ergodically cover a volume. The qualitative features of the strike points of the file lines are determined by the mode numbers of the resonant perturbations. With low mode numbers a few large islands control the break up of the magnetic surfaces and the strike points lie within far sharper lines than when high mode numbers cause the break up. These features are studied using area preserving maps and the results are applied to the DIII-D divertor as an example.